CN110096762A - A kind of prediction of lathe rigging error and control method - Google Patents
A kind of prediction of lathe rigging error and control method Download PDFInfo
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Abstract
Description
技术领域technical field
本发明涉及数控机床装配测试领域,特别是涉及考虑了滚动导轨误差和结构件重力变形的机床装配误差预测与控制方法。The invention relates to the field of assembling and testing of numerically controlled machine tools, in particular to a method for predicting and controlling machine tool assembling errors taking into account rolling guide rail errors and gravity deformation of structural parts.
背景技术Background technique
高速、高精度、高可靠性的精密加工中心已经成为了现代装备制造业的发展方向[1],很多国家把发展精密数控机床作为发展高端制造业的首要任务。精密卧式加工中心作为一种重要的数控机床,具有自动化程度高、加工效率高等一系列优点,在航天、航空、精密模具加工等多种领域都有着广泛的应用。High-speed, high-precision, and high-reliability precision machining centers have become the development direction of modern equipment manufacturing [1]. Many countries regard the development of precision CNC machine tools as the primary task of developing high-end manufacturing. As an important CNC machine tool, the precision horizontal machining center has a series of advantages such as high degree of automation and high processing efficiency, and is widely used in aerospace, aviation, precision mold processing and other fields.
对于占据装配过程大量时间的导轨安装调整没有明确有效的指导方法,技术人员常常忽略考虑滚动结合面存在直线度等几何误差的作用下,导轨误差对滑块和运动部件的误差传递作用。同时,装配过程中零部件的重力变形对装配误差的影响很大,目前机床装配工作中常采用反变形策略进行补偿,但反变形的控制量不是很精准,且未能考虑导轨误差的传递作用,未能将变形偏差及导轨的均化作用与最终的装配误差间建立函数关系。There is no clear and effective guidance method for guide rail installation and adjustment, which takes up a lot of time in the assembly process. Technicians often ignore the effect of guide rail error on the error transmission of sliders and moving parts under the effect of geometric errors such as straightness on the rolling joint surface. At the same time, the gravity deformation of parts during the assembly process has a great influence on the assembly error. At present, the anti-deformation strategy is often used to compensate for the assembly work of machine tools, but the control amount of anti-deformation is not very accurate, and the transfer effect of the guide rail error is not considered. The functional relationship between the deformation deviation and the homogenization of the guide rail and the final assembly error cannot be established.
因此,当前传统的装配工艺主要依赖于工人经验,缺乏科学的理论分析与指导规范,装配可靠性难以保证,装配效率低。Therefore, the current traditional assembly process mainly relies on the experience of workers, lacks scientific theoretical analysis and guidance specifications, makes assembly reliability difficult to guarantee, and assembly efficiency is low.
[1]刘佳.数控机床装配故障率建模与控制技术研究[D].重庆:重庆大学,硕士学位论文,2012.[1] Liu Jia. Research on Modeling and Control Technology of Assembly Failure Rate of CNC Machine Tool [D]. Chongqing: Chongqing University, Master Thesis, 2012.
发明内容Contents of the invention
本发明的目的是为了克服现有技术中的不足,提供一种考虑了滚动导轨误差和结构件重力变形的机床装配误差预测与控制方法。通过对精密卧式加工中心的装配误差传递机理进行研究,综合考虑导轨误差和重力变形的影响,建立装配误差传递模型,提出装配误差控制调整方法,为精密卧式加工中心装配误差预测控制提供理论依据,科学指导机床装配人员工作,大幅提高我国精密机床装配精度和装配速度。The object of the present invention is to overcome the deficiencies in the prior art, and provide a machine tool assembly error prediction and control method that considers the error of the rolling guide rail and the gravity deformation of the structural parts. Through the research on the assembly error transmission mechanism of the precision horizontal machining center, comprehensively considering the influence of the guide rail error and the gravity deformation, the assembly error transmission model is established, and the assembly error control adjustment method is proposed to provide a theory for the assembly error prediction control of the precision horizontal machining center According to the scientific guidance of machine tool assembly personnel, the assembly accuracy and assembly speed of my country's precision machine tools have been greatly improved.
本发明的目的是通过以下技术方案实现的:The purpose of the present invention is achieved through the following technical solutions:
一种机床装配误差预测与控制方法,包括以下步骤:A machine tool assembly error prediction and control method, comprising the following steps:
(1)以赫兹接触理论为基础,建立基于变形协调的滚动导轨误差-工作台误差传递模型,并进行线性化;(1) Based on the Hertz contact theory, a rolling guide error-table error transfer model based on deformation coordination is established and linearized;
(2)针对精密卧式加工中心,借助ABAQUS仿真软件建立有限元模型,提取各部件在各装配步下的重力变形结果;(2) For the precision horizontal machining center, use the ABAQUS simulation software to establish a finite element model, and extract the gravity deformation results of each component under each assembly step;
(3)以基于微分矢量法的装配体误差模型为基础,建立考虑各部件重力变形和导轨误差的整机装配误差传递模型;(3) Based on the assembly error model based on the differential vector method, an assembly error transfer model of the whole machine is established considering the gravity deformation of each component and the error of the guide rail;
(4)针对所建立的整机装配误差传递模型,提出相应的装配误差调整、控制策略。(4) According to the established assembly error transfer model of the whole machine, put forward the corresponding assembly error adjustment and control strategy.
进一步的,步骤(1)中建立基于变形协调的滚动导轨误差-工作台误差传递模型具体包括如下步骤:Further, in step (1), the establishment of a rolling guide error-worktable error transfer model based on deformation coordination specifically includes the following steps:
(101)在运动部件的重心处、台面上和各滑块的中心处建立坐标系并定义误差;(101) Establish a coordinate system and define errors at the center of gravity of the moving parts, on the table and at the center of each slider;
(102)求解滚柱变形量及接触力;(102) solving roller deformation and contact force;
(103)根据受力平衡建立误差传递模型;(103) Establishing an error transfer model according to the force balance;
(104)线性化误差传递模型。(104) Linearize the error transfer model.
进一步的,步骤(2)具体包括以下步骤:Further, step (2) specifically includes the following steps:
(201)设定装配步与选取空间位置;(201) setting the assembly step and selecting the spatial position;
(202)提取各装配步部件重力变形;(202) Extract the gravity deformation of each assembly step part;
(203)计算重力变形导致的直线度偏差和角度偏差。(203) Calculate straightness deviation and angle deviation caused by gravity deformation.
进一步的,步骤(3)具体包括以下步骤:Further, step (3) specifically includes the following steps:
(301)将子装配体之间的装配结合面定义为装配误差传递模型中的关键产品特征;定义各关键产品特征的几何偏差状态;(301) Define the assembly joint surface between the sub-assemblies as the key product feature in the assembly error transfer model; define the geometric deviation state of each key product feature;
(302)以一个三零件构成的装配体为例,推导装配误差传递模型;(302) Taking an assembly composed of three parts as an example, deduce an assembly error transfer model;
(303)建立卧式加工中心整机装配误差传递模型。(303) Establish an assembly error transmission model of the horizontal machining center.
进一步的,步骤(301)中关键产品特征包括:床身立柱结合面相对于参考坐标系的偏差、立柱的X轴导轨安装平面相对于床身立柱结合面的垂直度偏差、X轴导轨的滑块表面的偏差、滑板的Y轴导轨安装平面相对于滑板滑块结合面的平行度偏差、Y轴导轨的滑块表面的偏差、主轴端相对于主轴箱滑块结合面的平行度偏差、床身的Z轴导轨安装平面相对于参考坐标系的偏差、Z轴导轨的滑块表面的偏差和工作台上表面相对于工作台滑块结合面的平行度偏差。Further, the key product features in step (301) include: the deviation of the joint surface of the bed column relative to the reference coordinate system, the perpendicularity deviation of the X-axis guide rail installation plane of the column relative to the joint surface of the bed column, and the slider of the X-axis guide rail. Surface deviation, the parallelism deviation of the installation plane of the Y-axis guide rail of the slide plate relative to the joint surface of the slide plate slider, the deviation of the slider surface of the Y-axis guide rail, the parallel deviation of the spindle end relative to the joint surface of the headstock slider, and the bed The deviation of the Z-axis guide rail installation plane relative to the reference coordinate system, the deviation of the slider surface of the Z-axis guide rail, and the parallelism deviation of the upper surface of the worktable relative to the joint surface of the worktable slider.
进一步的,步骤(4)具体包括以下步骤:Further, step (4) specifically includes the following steps:
(401)对已装配的装配体进行测量,获取其偏差状态;在现有装配体的偏差状态下,假设未装配的部件无误差,对整机末端偏差的状态进行预测,得到只考虑已装配部件误差的整机装配误差预测结果;(401) Measure the assembled assembly to obtain its deviation state; under the deviation state of the existing assembly, assuming that there is no error in the unassembled parts, predict the deviation state of the end of the whole machine, and obtain only the assembled Prediction results of machine assembly errors for component errors;
(402)对未装配的部件进行测量,获取其几何偏差,在现有装配体的偏差状态下,以未装配部件的偏差测量值代替未装配件的实际误差进行预测,得到考虑了所有子装配体误差的整机装配误差预测结果;(402) Measure the unassembled parts to obtain their geometric deviation. Under the deviation state of the existing assembly, use the deviation measurement value of the unassembled parts instead of the actual error of the unassembled parts to predict, and all subassemblies are considered Prediction results of assembly errors of the whole machine based on body errors;
(403)若只考虑已装配部件误差的整机装配误差预测结果的各项已超过要求的偏差状态,则对已装配的零部件进行调整;(403) If each item of the prediction result of the assembly error of the whole machine that only considers the error of the assembled parts has exceeded the required deviation state, adjust the assembled parts;
(404)若只考虑已装配部件误差得到的整机装配误差预测结果未超过要求的偏差状态,则继续判断考虑了所有子装配体误差情况下的整机装配误差预测结果是否超过要求的偏差状态,若已超过,则应对未装配的部件进行调整;直到步骤(403)和步骤(404)均不超过目标特征的偏差要求,则进行下一步装配,直到装配完成。(404) If the predicted result of the assembly error of the whole machine obtained by considering only the error of the assembled parts does not exceed the required deviation state, continue to judge whether the predicted result of the assembly error of the whole machine under the condition of considering all sub-assembly errors exceeds the required deviation state , if it has been exceeded, the unassembled parts should be adjusted; until step (403) and step (404) do not exceed the deviation requirement of the target feature, then proceed to the next step of assembly until the assembly is completed.
与现有技术相比,本发明的技术方案所带来的有益效果是:本发明综合考虑了滚动导轨几何误差对整机装配误差造成的影响,建立的整机装配误差预测模型与实际装配误差传递过程更贴切,更加符合客观装配情况;考虑了重力变形的可变性,在步骤(2)中提取了各部件在不同装配步下的变形结果,在步骤(3)建立的装配误差传递模型中计入不同装配步下的重力变形,可实现逐步预测;结合步骤(4)提出的精密机床装配策略,可以在装配过程中逐步控制各部件误差,减少反复刮研工作,可精准高效指导机床装配工作。Compared with the prior art, the beneficial effects brought by the technical solution of the present invention are: the present invention comprehensively considers the influence of the geometric error of the rolling guide rail on the assembly error of the complete machine, and the established assembly error prediction model of the complete machine is consistent with the actual assembly error. The transfer process is more appropriate and more in line with the objective assembly situation; considering the variability of gravity deformation, the deformation results of each component under different assembly steps are extracted in step (2), and the assembly error transfer model established in step (3) Taking into account the gravity deformation under different assembly steps, it can be predicted step by step; combined with the precision machine tool assembly strategy proposed in step (4), the error of each component can be gradually controlled during the assembly process, reducing repeated scraping work, and can accurately and efficiently guide machine tool assembly Work.
附图说明Description of drawings
图1为工作台及导轨滑块坐标系示意图;Figure 1 is a schematic diagram of the coordinate system of the workbench and the guide rail slider;
图2为机床的装配顺序示意图;Figure 2 is a schematic diagram of the assembly sequence of the machine tool;
图3为仿真中各部件的位置示意图;Fig. 3 is the schematic diagram of the position of each component in the simulation;
图4为立柱在各装配步中的Y向位移云图;Fig. 4 is the Y-direction displacement nephogram of the column in each assembly step;
图5为床身在各装配步中的Z向位移云图;Fig. 5 is the Z-direction displacement nephogram of the bed in each assembly step;
图6(a)为随装配步变化的X轴上导轨的Z向直线度误差曲线;Figure 6(a) is the Z-direction straightness error curve of the guide rail on the X-axis that changes with the assembly step;
图6(b)为随装配步变化的X轴上导轨的Y向直线度误差曲线;Figure 6(b) is the Y-direction straightness error curve of the guide rail on the X-axis that changes with the assembly step;
图7(a)为随装配步变化的X轴下导轨的Z向直线度误差曲线;Figure 7(a) is the Z-direction straightness error curve of the guide rail under the X-axis that changes with the assembly steps;
图7(b)为随装配步变化的X轴下导轨的Y向直线度误差曲线;Figure 7(b) is the Y-direction straightness error curve of the guide rail under the X-axis that changes with the assembly steps;
图8为随装配步变化的各轴导轨的绕X的转角误差值;Figure 8 is the error value of the rotation angle around X of the guide rails of each axis that changes with the assembly step;
图9为床身及Z轴导轨关键特征的坐标系与几何偏差示意图;Figure 9 is a schematic diagram of the coordinate system and geometric deviation of the key features of the bed and the Z-axis guide rail;
图10为立柱及X轴导轨关键特征的坐标系与几何偏差示意图;Figure 10 is a schematic diagram of the coordinate system and geometric deviation of the key features of the column and the X-axis guide rail;
图11为滑板及Y轴导轨关键特征的坐标系与几何偏差示意图;Figure 11 is a schematic diagram of the coordinate system and geometric deviation of the key features of the slide plate and the Y-axis guide rail;
图12为主轴箱及工作台关键特征的坐标系与几何偏差示意图;Figure 12 is a schematic diagram of the coordinate system and geometric deviation of the key features of the headstock and workbench;
图13为三零件装配体几何偏差与变形偏差的传递过程;Fig. 13 is the transmission process of geometric deviation and deformation deviation of three-part assembly;
图14为机床装配误差控制策略流程图。Figure 14 is a flow chart of the machine tool assembly error control strategy.
具体实施方式Detailed ways
以下结合附图和具体实施例对本发明作进一步详细说明。应当理解,此处所描述的具体实施例仅仅用以解释本发明,并不用于限定本发明。The present invention will be described in further detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described here are only used to explain the present invention, not to limit the present invention.
1滚动导轨误差-工作台误差传递模型建立1 Rolling guide error-worktable error transfer model establishment
1.1赫兹接触理论1.1 Hertz Contact Theory
根据赫兹接触理论可知,接触变形与接触压力之间的关系为:According to the Hertz contact theory, the relationship between contact deformation and contact pressure is:
在工程应用中,由于滚柱的受力很复杂,因此主要采用其经验公式(可参考文献:Zhupanska O I.Contact problem for elastic spheres:Applicability of the Hertztheory to non-small contact areas[J].International Journal of EngineeringScience,2011,49(7):576-588.):In engineering applications, because the force of the roller is very complicated, its empirical formula is mainly used (reference: Zhupanska O I. Contact problem for elastic spheres: Applicability of the Hertz theory to non-small contact areas[J].International Journal of Engineering Science, 2011, 49(7):576-588.):
其中,E1,E2是滚柱和滚道面的弹性模量;υ1,υ2是滚柱和滚道面的泊松比;R是滚柱的半径;l是滚柱的长度。Among them, E 1 , E 2 are the elastic modulus of the roller and the raceway surface; υ 1 , υ 2 are the Poisson's ratio of the roller and the raceway surface; R is the radius of the roller; l is the length of the roller.
滚柱与滚道一般均为钢材料,它们的弹性模量E和泊松比υ相同,则接触力Q是接触变形δn的函数:Rollers and raceways are generally made of steel, and their elastic modulus E and Poisson's ratio υ are the same, then the contact force Q is a function of contact deformation δ n :
其中,in,
对于滚动体来说,有两个接触点,变形在两个接触点上同时发生,属于双边变形,故根据赫兹接触理论的经验公式,可得滚动体ki的接触力:For the rolling element, there are two contact points, and the deformation occurs at the two contact points at the same time, which belongs to bilateral deformation. Therefore, according to the empirical formula of the Hertz contact theory, the contact force of the rolling element ki can be obtained:
其中,Fki为第i个截面上k滚道中的滚动体的接触力,其方向取决于接触角。Δdki滚柱的总变形量,E和υ分别为滚珠与滚道材料的弹性模量和泊松比。Among them, F ki is the contact force of the rolling elements in the k raceway on the i-th section, and its direction depends on the contact angle. Δd ki is the total deformation of the roller, E and υ are the elastic modulus and Poisson's ratio of the ball and the raceway material, respectively.
1.2滑块-移动部件间误差传递模型1.2 Error transfer model between slider and moving parts
1.2.1坐标系建立及各误差定义1.2.1 Establishment of coordinate system and definition of each error
针对目前机床常用的双导轨四滑块结构,首先,在运动部件的重心处、台面上和各滑块的中心处建立坐标系,如图1所示。工作台的重心相对安装平面,即滑块的上表面的距离为H1,台面坐标系距离重心为H2。导轨跨距为Lv,同一导轨上两滑块的距离为Lh。假设四个滑块的坐标系原点在运动部件坐标系下的坐标为[xr,j,yr,j,zr,j](j=1,2,3,4)。For the structure of double guide rails and four sliders commonly used in machine tools at present, firstly, a coordinate system is established at the center of gravity of the moving parts, the table top and the center of each slider, as shown in Figure 1. The center of gravity of the worktable is relative to the installation plane, that is, the distance from the upper surface of the slider is H 1 , and the distance from the center of gravity of the table top coordinate system is H 2 . The span of the guide rail is L v , and the distance between two sliders on the same guide rail is L h . Assume that the coordinates of the origin of the coordinate system of the four sliders in the coordinate system of the moving part are [x r,j ,y r,j ,z r,j ] (j=1,2,3,4).
由于导轨误差会引起运动部件的位置和姿态误差,因此需要分别假设:Since the guideway error will cause the position and attitude errors of the moving parts, it is necessary to assume separately:
在滑块坐标系下,导轨误差为:In the slider coordinate system, the guide rail error is:
Δg,j=[δx,gj,δy,gj,θx,gj,θy,gj,θz,gj]T (7)Δ g,j =[δ x,gj ,δ y,gj ,θ x,gj ,θ y,gj ,θ z,gj ] T (7)
在运动部件坐标系下,运动部件中心的误差为:In the coordinate system of the moving part, the error of the center of the moving part is:
Δt=[δx,t,δy,t,θx,t,θy,t,θz,t]T (8)Δ t = [δ x,t ,δ y,t ,θ x,t ,θ y,t ,θ z,t ] T (8)
1.2.2滚柱变形量及接触力求解1.2.2 Roller deformation and contact force solution
在不考虑运动部件的变形的情况下,在运动部件坐标系中,滑块j中任意截面i上的滑块滚道k与滚柱的接触点Ar,jki=[xr,jki,yr,jki,zr,jki]T,由于误差的影响会移动到Ar.j′=[xr,jki′,yr,jki′,zr,jki′]T,即:Without considering the deformation of the moving parts, in the coordinate system of the moving parts, the contact point A r,jki =[x r,jki ,y of the slider raceway k and the roller on any section i in the slider j r,jki ,z r,jki ]T, will move to A rj ′=[x r,jki ′,y r,jki ′,z r , jki ′]T due to the influence of the error, namely:
同样,在滑块坐标系下,导轨误差会引起滑块j中任意截面i上的导轨滚道k与滚柱的接触点Ag=[xg,jki,yg,jki,zg,jki]T会移动到Ag′=[xg,jki′,yg,jki′,zg,jki′]T,则:Similarly, in the slider coordinate system, the error of the guide rail will cause the contact point A g of the guide rail raceway k and the roller on any section i of the slider j = [x g,jki ,y g,jki ,z g,jki ]T will move to A g ′=[x g,jki ′,y g,jki ′,z g,jki ′]T, then:
将其统一到运动部件坐标系下,可以求得Ag与Ar.j′之间的距离变化为:Unifying it into the coordinate system of moving parts, the distance change between A g and A rj ′ can be obtained as:
其中Δdpre为滚动体的预紧量,xr,j与yr,j为j滑块的坐标系原点在运动部件坐标系下的X与Y向坐标。Where Δd pre is the preload of the rolling body, x r, j and y r, j are the X and Y coordinates of the origin of the coordinate system of the j slider in the coordinate system of the moving part.
根据公式(5)-(6),可以求得滚柱的接触力为:According to formulas (5)-(6), the contact force of the roller can be obtained as:
1.2.3受力平衡分析建立误差传递模型1.2.3 Force balance analysis to establish error transfer model
在运动部件坐标系下,可以求得所有滚柱的接触合力和合力矩,假设运动部件中心处受到外力Fx,t,Fy,t和外力距Mx,t,My,t,Mz,t的作用,根据系统受力平衡,可以建立如下平衡方程:In the coordinate system of the moving part, the resultant contact force and resultant moment of all rollers can be obtained, assuming that the center of the moving part is subjected to the external force F x,t ,F y,t and the external force distance M x,t ,M y,t ,M z ,t , according to the force balance of the system, the following balance equation can be established:
根据式(13),已知四滑块所在位置的误差Δg,j=[δx,gj,δy,gj,θx,gj,θy,gj,θz,gj]T的条件下,联立公式(9)-(13)可以求得运动部件的五维误差Δt=[δx,t,δy,t,θx,t,θy,t,θz,t]T。According to the formula (13), it is known that the error Δ g,j of the position of the four sliders =[δ x,gj ,δ y,gj ,θ x,gj ,θ y,gj ,θ z,gj ] T , Simultaneous formulas (9)-(13) can obtain the five-dimensional error Δt=[δ x,t ,δ y,t ,θ x,t ,θ y,t ,θ z,t ] T of the moving parts.
用下述公式(14)代表运动部件误差与四滑块各自误差之间的关系,即:The following formula (14) is used to represent the relationship between the error of the moving parts and the respective errors of the four sliders, namely:
Δt=G(Δg,1,Δg,2,Δg,3,Δg,4) (14) Δt = G(Δg ,1, Δg ,2, Δg ,3 ,Δg ,4 ) (14)
Δg,j=[δx,gj,δy,gj,θx,gj,θy,gj,θz,gj]T为滑块j的误差,Δt=[δx,t,δy,t,θx,t,θy,t,θz,t]T为运动部件的误差。Δ g,j =[δ x,gj ,δ y,gj ,θ x,gj ,θ y,gj ,θ z,gj ] T is the error of slider j, Δ t =[δ x,t ,δ y ,t ,θ x,t ,θ y,t ,θ z,t ] T is the error of the moving parts.
1.2.4误差传递模型线性化1.2.4 Error transfer model linearization
上述模型是一个非线性的模型,虽能够较精确的描述四滑块误差与运动部件误差的传递关系。但由于非线性关系在分析中难以处理,不利于对整机装配误差的预测,因此采用多元线性回归的方法进行线性化处理。通过进行显著性分析确定必要的变量,进而使用Matlab求取线性回归矩阵$,即Δt与Δg,1,Δg,2,Δg,3,Δg,4间满足下列关系:The above model is a nonlinear model, although it can more accurately describe the transfer relationship between the error of the four sliders and the error of the moving parts. However, because the nonlinear relationship is difficult to deal with in the analysis, it is not conducive to the prediction of the assembly error of the whole machine, so the method of multiple linear regression is used for linearization. Determine the necessary variables by performing significance analysis, and then use Matlab to obtain the linear regression matrix $, that is, the relationship between Δ t and Δ g,1 , Δ g,2 , Δ g,3 , Δ g,4 satisfies the following relationship:
于是,建立起运动部件与滑块之间的误差传递线性化模型,已知四滑块所在位置的误差Δg,j=[δx,gj,δy,gj,θx,gj,θy,gj,θz,gj]T的条件下,利用公式(15)可以求得运动部件的五维误差Δt=[δx,t,δy,t,θx,t,θy,t,θz,t]T。Therefore, the error transfer linearization model between the moving part and the slider is established, and the error Δ g,j of the position of the four sliders is known = [δ x,gj ,δ y,gj ,θ x,gj ,θ y ,gj ,θ z,gj ] T , the five-dimensional error Δ t = [δ x,t ,δ y,t ,θ x,t ,θ y,t can be obtained by formula (15) ,θ z,t ] T .
2.整机装配变形的有限元仿真2. Finite element simulation of machine assembly deformation
机床装配过程中,各结构件重力作用会导致结合面产生变形或位移,对机床整机装配误差产生影响。由于装配变形无法通过测量的手段获得,下面通过Abaqus仿真软件对结构件重力变形进行了提取。During the machine tool assembly process, the gravity of each structural part will cause deformation or displacement of the joint surface, which will affect the assembly error of the machine tool. Since the assembly deformation cannot be obtained by means of measurement, the gravity deformation of the structural parts is extracted through the Abaqus simulation software below.
2.1装配步设定与空间位置选取2.1 Assembly step setting and spatial location selection
由于各结构件是逐步装配的,因此随着装配步的改变,重力变形的结果有所不同,需针对各装配步分别求取其重力变形结果,各装配步内容如图2所示;同时由于各运动结构件处在不同的空间位置时会不同程度的影响导轨的静变形状态,在每个导轨轴选取3个位置(如图3所示,每个导轨选取的三个位置分别用0、1和2表示),便可以获得三个位置的仿真数据,然后可以用多项式拟合将其余的位置计算出来,即可获得任意位置的变形或位移。Since each structural part is assembled step by step, the results of gravity deformation are different with the change of assembly steps, and the results of gravity deformation need to be obtained for each assembly step. The content of each assembly step is shown in Figure 2; at the same time, due to When the moving structural parts are in different spatial positions, they will affect the static deformation state of the guide rail to varying degrees. Three positions are selected for each guide rail axis (as shown in Figure 3, the three positions selected for each guide rail are respectively 0, 1 and 2), the simulation data of three positions can be obtained, and then the remaining positions can be calculated by polynomial fitting, and the deformation or displacement of any position can be obtained.
2.2各装配步部件变形提取2.2 Deformation extraction of components in each assembly step
以立柱的上下导轨为例,获得其在各装配步中的变形云图如图4-5。Taking the upper and lower guide rails of the column as an example, the deformation cloud diagram obtained in each assembly step is shown in Figure 4-5.
2.3计算重力导致的直线度、角度偏差2.3 Calculate the straightness and angle deviation caused by gravity
通过有限元分析的位移变化结果,可以分离出装配步中变形引起的导轨直线度误差和绕X轴的角度误差。对于直线度误差,直接减去同一导轨上的最低点即可。对于绕X轴的转角误差,X轴导轨为上导轨端点与下导轨同一端点的差值,再除以导轨跨距,Y、Z轴导轨为同一导轨两端点的差值除以导轨长度。Through the displacement change results of the finite element analysis, the straightness error of the guide rail and the angular error around the X axis caused by the deformation in the assembly step can be separated. For straightness error, simply subtract the lowest point on the same rail. For the rotation angle error around the X axis, the X-axis guide rail is the difference between the end point of the upper guide rail and the same end point of the lower guide rail, and then divided by the span of the guide rail, and the Y and Z-axis guide rails are the difference between the two ends of the same guide rail divided by the length of the guide rail.
以立柱导轨为例,其分离后的直线度结果如图6(a)至图7(b),各轴导轨绕X轴的转角如图8。Taking the column guide rail as an example, the straightness results after separation are shown in Figure 6(a) to Figure 7(b), and the rotation angles of the guide rails around the X axis are shown in Figure 8.
3.基于微分矢量法建立整机误差模型3. Establish the error model of the whole machine based on the differential vector method
3.1各特征几何偏差状态定义3.1 Definition of geometric deviation state of each feature
由于整个装配体的偏差主要是由子装配体之间的结合面偏差决定的,通常将子装配体之间的装配结合面定义为装配误差传递模型中的关键产品特征。表1所示为定义的所有关键产品特征,特征具体位置如图9-12所示。Since the deviation of the whole assembly is mainly determined by the joint surface deviation between subassemblies, the assembly joint surface between subassemblies is usually defined as a key product feature in the assembly error transfer model. Table 1 shows all the key product features defined, and the specific positions of the features are shown in Figure 9-12.
表1各结合面几何偏差的符号与含义Table 1 Symbols and meanings of the geometric deviations of each joint surface
在三维空间中,每个特征都有六个方向的自由度,即沿三个坐标轴方向的平移自由度和绕三个坐标轴旋转自由度。进而,特征k相对于其理论位置和方向的偏差状态可以用一个6×1的向量表示,即:In three-dimensional space, each feature has six degrees of freedom, that is, translational degrees of freedom along three coordinate axes and rotational degrees of freedom around three coordinate axes. Furthermore, the deviation state of feature k relative to its theoretical position and orientation can be represented by a 6×1 vector, namely:
[Pk Qk]T=[ΔXk,ΔYk,ΔZk,Δθxk,Δθyk,Δθzk]T (16)[P k Q k ] T = [ΔX k ,ΔY k ,ΔZ k ,Δθ xk ,Δθ yk ,Δθ zk ] T (16)
其中,k表示特征编号。Among them, k represents the feature number.
考虑形位误差和重力变形同时存在的情况,对于特征的偏差状态,需要引入i表示装配步,即:Considering the simultaneous existence of shape error and gravity deformation, for the deviation state of the feature, it is necessary to introduce i to represent the assembly step, namely:
定义当i=0为未装配状态,当i=k为第k个零件装配之后的状态。Define when i=0 is the unassembled state, when i=k is the state after the kth part is assembled.
首先,由于特征的自身几何偏差不随装配步变化,定义其为:First, since the geometric deviation of the feature itself does not change with the assembly step, it is defined as:
其中,δk为微分平移矢量,εk微分旋转矢量。Among them, δ k is the differential translation vector, and ε k is the differential rotation vector.
由于特征受重力变形而产生的偏差会随装配步而改变,将其记为:The deviation due to the deformation of the feature due to gravity varies with the assembly step and is written as:
其中,为微分平移矢量,微分旋转矢量。in, is the differential translation vector, Differential rotation vector.
3.2以一个三零件构成的装配体为例,推导装配误差传递模型一般形式3.2 Taking an assembly composed of three parts as an example, deduce the general form of the assembly error transfer model
由微分矢量法可知:It can be known from the differential vector method that:
R为3x3的旋转矩阵,D为3x3的平移矩阵,d为对应方向的距离向量。上下角标表示发生变换的两个坐标系。R is a 3x3 rotation matrix, D is a 3x3 translation matrix, and d is a distance vector in the corresponding direction. The upper and lower subscripts indicate the two coordinate systems in which the transformation takes place.
如图13所示:As shown in Figure 13:
第一步装配时,面1尚未产生变形,仅有几何偏差:In the first step of assembly, surface 1 has not yet been deformed, only geometric deviation:
第二步装配时,重力变形产生的偏差与几何偏差叠加,面1的偏差为:In the second step of assembly, the deviation caused by gravity deformation is superimposed on the geometric deviation, and the deviation of surface 1 is:
而面2的偏差为:And the deviation of surface 2 is:
同理可以推广特征k在i步装配完成后的偏差状态为:Similarly, the deviation state of feature k after the i-step assembly can be extended as:
而在整机装配完成后,即n步装配完成后,特征k的偏差状态为:After the assembly of the whole machine is completed, that is, after the n-step assembly is completed, the deviation state of feature k is:
应当注意的是,由于变形偏差状态与装配步有关,特征k的中间状态与完成装配后的状态不同,即:It should be noted that since the deformation deviation state is related to the assembly step, the intermediate state of feature k is different from the state after the completion of assembly, namely:
当装配体的n个装配子体全部装配完成,所有特征的状态均变为则特征n的偏差为:When all n assembly sub-bodies of the assembly are assembled, the status of all features changes to Then the deviation of feature n is:
3.3精密卧式加工中心整机装配误差传递模型建立3.3 Establishment of assembly error transfer model of precision horizontal machining center
由于精密卧式加工中心是由两个开环装配组成的闭环装配体,分别求取主轴的偏差和工作台的偏差,即可求得整机的装配误差传递模型。下面主要以主轴的偏差状态为例进行推导。Since the precision horizontal machining center is a closed-loop assembly composed of two open-loop assemblies, the deviation of the main shaft and the deviation of the worktable can be calculated separately to obtain the assembly error transfer model of the whole machine. The following mainly takes the deviation state of the main shaft as an example for derivation.
当床身立柱结合面具有几何偏差,则其偏差状态为:When the joint surface of the bed column has a geometric deviation, the deviation state is:
根据式(25),当立柱和X轴导轨装配后,X轴导轨滑块表面的偏差状态既受到自身几何偏差的影响,也受到床身立柱结合面和X轴导轨安装面的影响,因此X轴导轨滑块的偏差状态为:According to formula (25), when the column and the X-axis guide rail are assembled, the deviation state of the slider surface of the X-axis guide rail is not only affected by its own geometric deviation, but also by the joint surface of the bed column and the installation surface of the X-axis guide rail, so X The deviation state of the shaft guide slider is:
下标sj表示滑板滑块j;δsj,εsj分别为滑板滑块的位置误差和转角误差向量。The subscript sj represents the slider j of the skateboard; δ sj and ε sj are the position error and rotation angle error vectors of the slider respectively.
根据滑板与带动其运动的滑块之间的线性回归误差模型可以推导出滑板的偏差状态为:According to the linear regression error model between the skateboard and the slider that drives it, the deviation state of the skateboard can be deduced as:
其中Bsj(j=0,1..4)的为滑板回归系数矩阵中对应滑块j的矩阵。Among them, B sj (j=0,1..4) is the matrix corresponding to slider j in the skateboard regression coefficient matrix.
同理,考虑滑板误差、主轴箱滑块误差对主轴的影响,主轴的偏差状态为:Similarly, considering the influence of the slider error and the headstock slider error on the spindle, the deviation state of the spindle is:
其中,Bbj表示主轴箱滑块j的线性回归系数矩阵,δbj,εbj分别为主轴箱滑块的位移误差和转角误差向量。Among them, B bj represents the linear regression coefficient matrix of the headstock slider j, and δ bj and ε bj are the displacement error and rotation angle error vectors of the headstock slider respectively.
同理,工作台的偏差状态为:Similarly, the deviation state of the workbench is:
At,mj=BtjW5,tj,At,nj=BtjW6,tj,At,kj=BtjWtj,tj A t,mj =B tj W 5,tj ,A t,nj =B tj W 6,tj ,A t,kj =B tj W tj,tj
其中,Btj表示工作台滑块j的线性回归系数矩阵,δtj,εtj分别为工作台滑块的位移误差和转角误差向量。Among them, B tj represents the linear regression coefficient matrix of the worktable slider j, and δ tj and ε tj are the displacement error and rotation angle error vectors of the worktable slider respectively.
精密卧式加工中心是由两个装配开环组成的闭环装配体,因此将主轴和工作台的偏差旋转到同一坐标系下,即可求得工作台和主轴间相对偏差为:The precision horizontal machining center is a closed-loop assembly composed of two assembly open loops. Therefore, by rotating the deviation of the spindle and the worktable to the same coordinate system, the relative deviation between the worktable and the spindle can be obtained as:
4.装配误差预测与控制策略4. Assembly error prediction and control strategy
面向过程的装配误差控制,是以控制每一装配步的误差为手段,实现最终误差满足要求的一种方法。根据所建立的模型,在机床装配过程中,每进行一次安装,均可以对目标特征的偏差和误差进行预测,同时可以分析出已装配的零部件对目标特征的影响程度,因此可以如下的装配误差控制策略。Process-oriented assembly error control is a method to control the error of each assembly step to achieve the final error to meet the requirements. According to the established model, in the process of machine tool assembly, the deviation and error of the target feature can be predicted for each installation, and at the same time, the degree of influence of the assembled parts on the target feature can be analyzed, so the assembly can be as follows error control strategy.
第一步:对已装配的装配体进行测量,获取其偏差状态[Pk,Qk]T;在现有组装体的偏差状态[Pk,Qk]T下,假设未装配的部件无误差,对末端偏差的状态进行预测,得到只考虑已装配体误差的整机装配误差预测结果 Step 1: Measure the assembled assembly to obtain its deviation state [P k , Q k ] T ; under the deviation state [P k , Q k ] T of the existing assembly, it is assumed that the unassembled parts have no Error, predict the state of the end deviation, and obtain the prediction result of the assembly error of the whole machine that only considers the error of the assembled body
第二步:对未装配的部件进行测量,获取其几何偏差[δk+1,εk+1]T。在现有组装体的偏差状态[Pk,Qk]T下,以未装配部件的偏差测量值代替未装配件的实际误差进行预测,得到考虑了所有子装配体误差的整机装配误差预测结果 The second step: measure the unassembled parts to obtain their geometric deviation [δ k+1 ,ε k+1 ] T . Under the deviation state [P k , Q k ] T of the existing assembly, the deviation measurement value of the unassembled parts is used to replace the actual error of the unassembled parts for prediction, and the assembly error prediction of the whole machine is obtained considering the errors of all sub-assemblies result
第三步:若只考虑已装配部件误差的整机装配误差预测结果的各项已超过要求的偏差状态则必须对已装配的零部件进行调整。Step 3: If only the error of the assembled parts is considered, the prediction result of the assembly error of the whole machine Items of have exceeded the required deviation status Then the assembled parts must be adjusted.
第四步:若只考虑已装配部件误差得到的整机末端误差预测结果未超过则继续判断考虑了所有子装配体误差情况下的整机装配误差预测结果是否超过若已超过,则应对未装配的部件进行调整。可以通过分析两种预测结果(与)的各项变化,判断各项误差来源以及其受已装配部件的影响大还是未装配的部件影响大,对影响大的误差源进行调整,直到第三步和第四步均不超过目标特征的偏差要求,则进行下一步装配,直到装配完成。Step 4: If only the error of the assembled parts is considered, the prediction result of the end error of the whole machine not exceeded Then continue to judge the assembly error prediction results of the whole machine considering all sub-assembly errors Is it more than If exceeded, adjustments should be made to unassembled components. It can be analyzed by analyzing two prediction results ( and ), determine the source of each error and whether it is greatly affected by the assembled parts or the unassembled parts, and adjust the error source with a large influence until the third step and the fourth step do not exceed the target feature If the deviation requirements are met, proceed to the next step of assembly until the assembly is completed.
上述装配误差控制策略的流程如下图14所示。The process flow of the above assembly error control strategy is shown in Figure 14 below.
本发明并不限于上文描述的实施方式。以上对具体实施方式的描述旨在描述和说明本发明的技术方案,上述的具体实施方式仅仅是示意性的,并不是限制性的。在不脱离本发明宗旨和权利要求所保护的范围情况下,本领域的普通技术人员在本发明的启示下还可做出很多形式的具体变换,这些均属于本发明的保护范围之内。The present invention is not limited to the embodiments described above. The above description of the specific embodiments is intended to describe and illustrate the technical solution of the present invention, and the above specific embodiments are only illustrative and not restrictive. Without departing from the gist of the present invention and the scope of protection of the claims, those skilled in the art can also make many specific changes under the inspiration of the present invention, and these all belong to the protection scope of the present invention.
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